I am going to be brutally honest with you:
If you have bad grades it is unlikely that you will get an offer from the LSE, it is a very selective school (probably one of the most selective in the country)
If you find it difficult to have good grades in high school or to get an offer from LSE, let me tell you that investment banking is absurdly selective. I study at LSE, the vast majority of my classmates are smart and hard-working and yet many struggle to find a job in IB or consulting.
The price of higher education in the UK is crazy. You said you live in Luxembourg so I assume you don't have British citizenship. To study at LSE as an international student, you have to pay between 15k and 30k per year in academic fees (depending on the degree). If you live in LSE accommodations, it is between 10k and 12k of additional fees per year (but still less expensive than most private accommodations in London). Don't expect to pay 35k for your degree, it will be closer to 90k.
If you really want to study abroad, I suggest you apply to universities in continental European countries. France, the Netherlands and Germany have amazing universities where you can study for 1k per year.